About Rating Systems

 RATING BACKGROUND

These ratings are designed to provide an accurate rating for Wisconsin high school sports. The ratings are designed such that a team's rating will improve when they perform better than expected. The expectation for a team's performance is based on their current rating and their opponent's rating.

Beating a better opponent will cause a rating to increase more than beating a worse opponent. Additionally, losing to a better opponent will cause a lower rating decrease than losing to a worse opponent.

Rating Formulas

The rating system uses capped point differential (CPD). This metric is a game's margin of victory capped at a certain point value.

Capping Values:

• Basketball - 20 Points
• Soccer - 4 Goals
• Football - 25 Points
• Baseball - 7 Runs
• Softball - 8 Runs

Basketball Formulas:

Capped Point Differential (CPD) = MAX [-20, MIN[ 20, Team A Score - Team B Score]]

Adjusted CPD (aCPD) = [CPD + 20] / 40

An expected aCPD value is calculated based on each team's rating prior to the game. This value reflects how a team "should" perform in a game:

Expected aCPD = 1 / (10^(-(Team A Rating - Team B Rating)/175) + 1)

The aCPD result from a game is compared to the expected aCPD to determine the new rating for each team:

New Rating = Old Rating + 75 x [ Actual aCPD - Expected aCPD ]

The value of 75 in the above formula is known as game power: the maximum amount that a team's rating can change from a single game.

Example Game: 

Team A and Team B both have a current rating of 1000.

The game is expected to be a tie (because they have the same rating). This produces an expected CPD of 0 and an expected aCPD of 0.50.

Team A wins by 8 points. Their CPD is 8; their aCPD is 0.70. Team B's CPD is -8; their aCPD is 0.30.

Team A New Rating = 1000 + 75 * [0.70 - 0.50] = 1000 + 15 = 1015

Team B New Rating = 1000 + 75 * [0.30 - 0.50] = 1000 - 15 = 985

Development

The rating system was developed using actual game results from previous seasons. No data from the ranking season was used to develop the system. The prior seasons were used to establish and test the rating formulas. They were also used to generate a starting value for each team for the current seasons.

Several versions of ratings were tested including a simple version that only used wins and losses. Ultimately, using the capped point differential rating system described above was the most predictive of future wins and losses.

The rating accuracy for basketball:

The ratings can be used to estimate the win probably between two boys basketball teams:

The ratings are further broken out into an O-Rating (offense) and a D-Rating (defense). The difference between a team's O-Rating and their opponent's D-Rating produces an accurate estimate of projected points scored:

Modifications

Volleyball does not use capped point differential. Instead, the percent of games won during a match is compared against the expected percent of games won. Volleyball does not have O-Rating and D-Rating. Additionally, the game power of each match varies based on the match length:

• Best of 5 - 75 Points
• Best of 3 - 50 Points
• Best of 1 - 25 Points

Baseball uses a game power of 50. A single game of baseball is not as predictive of future results as a single game of other sports.

Additional Notes

Ratings are only created for teams involved with the WIAA. Out of state teams and Wisconsin teams that are non-WIAA are not provided a rating.

Results from games involving a non-rated team are ignored.

Forfeits (reflected as scores of 2-0) are ignored when possible.

The rating for a new season is 70% of the prior season's final rating and 30% of the average rating for the team's division (based on school size).

New teams are assigned a judgement-based initial rating.